4n^2+6n-2000=0

Solution for 4n^2+6n-2000=0 equation:

4n^2+6n-2000=0

a = 4; b = 6; c = -2000;
Δ = b2-4ac
Δ = 62-4·4·(-2000)
Δ = 32036
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32036}=\sqrt{4*8009}=\sqrt{4}*\sqrt{8009}=2\sqrt{8009}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{8009}}{2*4}=\frac{-6-2\sqrt{8009}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{8009}}{2*4}=\frac{-6+2\sqrt{8009}}{8}
$